To find the equation of a line passing through two points, we use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

where $m$ is the slope, and $(x_1, y_1)$ is one of the points on the line. The slope $m$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Step 1: Find the slope

Using the points $(-4, 3)$ and $(3, 5)$: $m = \frac{5 - 3}{3 - (-4)} = \frac{2}{7}$

Step 2: Use the slope and one point in the point-slope form

We can use the point $(-4, 3)$:

$y - 3 = \frac{2}{7}(x - (-4))$

Simplifying the equation:

$y - 3 = \frac{2}{7}(x + 4)$

Step 3: Expand and simplify to the slope-intercept form

$y - 3 = \frac{2}{7}x + \frac{8}{7}$

Add 3 to both sides:

$y = \frac{2}{7}x + \frac{8}{7} + 3$

Convert 3 to a fraction:

$y = \frac{2}{7}x + \frac{8}{7} + \frac{21}{7}$

$y = \frac{2}{7}x + \frac{29}{7}$

Thus, the equation of the line is:

$y = \frac{2}{7}x + \frac{29}{7}$

Would you like further explanation on any of the steps?

Here are 5 related questions to further your understanding:

1. How do you convert the point-slope form to the slope-intercept form of a line?
2. What is the significance of the slope in a linear equation?
3. How can you find the equation of a line if you know the slope and only one point?
4. How do parallel lines compare in terms of slope?
5. How would the equation change if the line passed through different points?

Tip: Remember, the slope represents the rate of change of $y$ with respect to $x$. A positive slope means the line ascends from left to right!